Applied Mathematics and Control Sciences

It is shown that the solution of certain problems of the dynamics appropriate and often the only acceptable is the presentation of the state of the object in a superposition of its boundary conditions, and the intermediate state depends on the values of state functions that characterize the variability of the state of the object. It was noted that in many cases are non-linear function of the state, and their analytical representation often unknown, but for the model with mutually by equal boundary conditions state function, as a rule, are continuous and monotone on the interval studied, and the value of state functions varies from zero to unity; under these conditions, the state function in almost any way are investigated for the analytical range and can be represented as a series expansions, for example Taylor. It is shown that the characteristic type of practical problems which can be solved using the proposed method is to calculate the dynamics of bulk cargo platform in the commission of linear oscillations in a horizontal plane; main difficulty of this problem is the lack of even approximate data on dynamic friction coefficient of the generalized because its value significantly affect fragments move cargo in its entirety, and not only in the plane of contact with the platform. It is shown that the representation of the cargo as a superposition of its movable and stationary states can solve this and similar problems.

In this paper an approach for customizing genetic algorithm for solving problem of planning line production is proposed. For this purpose, the criteria of efficiency and effectiveness of the genetic algorithm are introduced. Efficiency characterizes the ability of a genetic algorithm to find the global extremum in a given optimization problem. Effectiveness characterizes the rate at which the genetic algorithm allows to solve the optimization problem. Customizing genetic algorithm is done by selecting the best combination of several variants of genetic operators. For the production line bottling the example of the planning problem solution was considered. This example showed the feasibility and practical relevance of the proposed approach to the customizing of genetic algorithms. As a result of the significant number of numerical experiments were found arguments supporting the hypothesis of scalability customized genetic algorithm.

The main components of mass appraisal system of property for tax purposes and requirements arising from the principles of taxation are considered in the article. The problems of constructing a computer mass appraisal are analyzed in the article and ways to solve them are offered.